All Topological Bands of All Stoichiometric Materials

Abstract

The recently introduced theories of Topological Quantum Chemistry and Symmetry-Based Indicators (SIs) have facilitated the discovery of novel stable topological phases of matter and largescale searches for materials with experimentally accessible topological properties at the Fermi energy (EF ). In this work, we have completed the first catalog of stable and fragile topology in all of the bands both at and away from EF in the Inorganic Crystal Structure Database (ICSD), which we have made accessible through a substantial upgrade of Topological Materials Database (https://www.topologicalquantumchemistry.com/). We have computed the electronic structure, topological class, and stable and fragile SIs of all bands in the 96,196 processable ICSD entries with stoichiometric chemical formulas in the presence and absence of spin-orbit coupling, which we have grouped into 38,298 unique materials by common chemical formulas, crystal structures [space groups (SGs)], and topology at EF . Our calculations represent the completion of the symmetry-indicated band topology of known nonmagnetic materials, and a doubling of the number of materials accessible in previous topological material catalogs. Through our calculations, we discover the existence of novel classes of topological materials, including enforced topological semimetals with energetically isolated fragile bands at EF , repeat-topological (RTopo) materials with stable topological insulating gaps at and just below EF , and supertopological (STopo) materials in which every energetically isolated set of bands above the core shell is stable topological. Our findings recontextualize several previous experimental investigations of topological materials. We find that the transition-metal chalcogenides Ta2NiSe5 in SG 15 (C/2c) and Ta2NiSe7 in SG 12 (C2/m) -respectively previously highlighted for hosting exciton-insulator and charge-density-wave phases -are 3D topological insulators (TIs) in their normal states. Additionally, we find that the higher-order TI rhombohedral bismuth in SG 166 (R 3m) and the indirect-gap TI Bi2Mg3 in SG 164 (P 3m1) are both RTopo and STopo materials. Previous ARPES investigations of Bi2Mg3 have demonstrated the presence of "surface resonance bands" below EF -in this work, we discover that the surface resonance bands are in fact RTopo Dirac-cone surface states. We present detailed statistics for our computations revealing that 52.65% of all materials are topological at EF , roughly 2/3 of bands across all materials exhibit symmetry-indicated stable topology, and that, shockingly, 87.99% of all materials contain at least one stable or fragile (crystalline) topological band in their spectrum (though potentially far from EF ). Our findings motivate the formulation of a new periodic table of chemical compounds based on the ubiquity of nontrivial electronic band topology in solid-state materials.

Three-Dimensional Real Space Invariants, Obstructed Atomic Insulators and A New Principle for Active Catalytic Sites

“…Using the above methods, based on the TQCDB [20,24], we have performed a high-throughput calculations for stoichiometric OAIs and OOAIs. As schematically shown in Fig.…”

“…Another example is the 3D Weyl semi-metal, which has Fermi arc states on the surface if the translation symmetry prohibiting hybridization between Weyl nodes is respected [10][11][12][13]. Whether a material is topologically nontrivial can be ef-ficiently diagnosed via the general theory of Topological quantum chemistry (TQC) [14,15] or the equivalent symmetry indicators [16][17][18][19] and the complete catalogues of topological materials were obtained in several works [20][21][22][23][24]. However, as the bulk band gaps of the topological materials are always small (in general, smaller than 0.3 eV), the surface states of topological materials have not been widely used in practical applications.…”

“…The EBRs are the induced representations into the space or magnetic group of the crystal from the irreducible representations (irreps) of the atomic orbitals sitting at the (maximal) high symmetry Wyckoff positions. We refer to the topology of this kind of symmetry-indicated topologically trivial insulator to as linear combination of EBRs (LCEBR) [20,23,24]. We emphasize that an insulator identified as LCEBR can also be a topological insulator or semimetal that cannot be diagnosed through symmetry eigenvalues at the highsymmetry momenta.…”

“…In the present work, we first develop a general framework to obtain the 3D RSIs in all the 1,651 Shubnikov space groups (SSGs) with spin-orbit coupling (SOC), including the 230 paramagnetic space groups (SGs) and the 1,421 magnetic space groups (MSGs), and provide the expressions of all the RSIs in the Bilbao Crystallographic Server (BCS). Compared with the RSIs in 2D wallpaper groups [29], the RSIs in 3D SSGs could be of Z 4 -type and composite, which are defined at multiple Wyckoff positions; moreover, the 3D RSIs are applicable to the 3D stoichiometric materials in the topological (magnetic) materials databases [20][21][22][23][24]. By applying the RSIs to all the (paramagnetic and magnetic) topologically trivial insulators on the respective Topological Quantum Chemistry website (TQCDB) and Topological Magnetic Materials website (MTQCDB), we perform a high-throughput search for paramagnetic OAIs, OOAIs and the magnetic OAIs (mOAIs).…”

Triple nodal points characterized by their nodal-line structure in all magnetic space groups

“…52-54. For each of the type-II magnetic space groups listed in Table II in Ref. 42, we performed a search of compounds with light elements (from the first three rows of the periodic system) on the Topological Materials Database [78][79][80]. By looking at the irreducible representation on high-symmetry points (for the case without spin-orbit coupling) and using the program Mcomprel [65][66][67] on the BCS, we inferred the ICRs and their dimension along the relevant HSL and identified crossings of 2D with 1D ICRs, i.e., TPs.…”